What is the aspect ratio of the content? The new iPhone5 is the first iPhone to have a modern Aspect ratio of 16:9, but all content is not in that aspect ratio. So there could be black bars on the top/bottom, or pillar boxes on the right/left depending on the aspect ratio of the source.

It's nothing to do with the source content. The app uses the old screen resolution, so a 16x9 video ends up being postage stamped on the iPhone 5 with black borders everywhere.

I'm sure they'll update the app, I just hope it's not a long wait for the update. In the mean time, you just have to remember the video is no smaller than on the iPhone 4; it's just not as big as it could be.